Supercritical airfoil sample sampling method and storage medium

Abstract

The application discloses a supercritical airfoil sample sampling method and a storage medium, and relates to the technical field of aviation. The method comprises the following steps: acquiring a sampling area, sampling according to the sampling area, and obtaining an expected sample set comprising expected samples; generating a first curve randomly according to each expected sample, and acquiring a first control point coordinate set corresponding to the first curve; performing airfoil optimization on the first control point coordinate set according to a multi-objective genetic algorithm for each expected sample, and obtaining estimated control point coordinates; mapping and taking values of the estimated control point coordinates through a buffet proxy model and a drag divergence proxy model respectively, and obtaining an estimated sample set corresponding to the expected sample set in a one-to-one manner; and calculating a surface pressure distribution map for machine learning according to the estimated sample set. The application can effectively guarantee the accuracy of the sample data set, and thus the design model established by machine learning can be effectively established.

Description

Technical Field

[0001] This application relates to the field of aerospace technology, and in particular to a supercritical airfoil sample sampling method and storage medium. Background Technology

[0002] In related technologies, supercritical airfoils are airfoils designed to increase the critical Mach number. They delay the dramatic increase in drag that occurs near the speed of sound, thereby increasing the aircraft's cruise speed. They are widely used in transonic aircraft such as commercial airliners. Currently, the cruise speeds of commercial airliners are all in the transonic range. In this speed range, shock waves appearing on the wing can induce boundary layer separation, causing periodic oscillations of the shock waves, also known as fluttering. Fluttering can generate unstable structural stresses in the airframe, reducing the aircraft's fatigue life and, in severe cases, potentially leading to the aircraft disintegrating in mid-air. The drag divergence Mach number represents the Mach number at which drag surges with increasing flight speed. This is a key parameter limiting the cruise speed of supercritical airfoils and determining fuel efficiency. The drag divergence Mach number is used to describe the drag divergence phenomenon.

[0003] To obtain supercritical airfoils that meet expectations and can be applied in practice, and to delay the occurrence of buffeting and drag divergence, a suitable design methodology for supercritical airfoils is crucial. Currently, design methods using machine learning to build design models have emerged, capable of fully considering the aerodynamic characteristics of airfoils through extensive data. However, machine learning requires large-scale data sampling. If the sample dataset used for machine learning is inaccurate, it is easy to fail to obtain a surface pressure distribution map for a suitable supercritical airfoil, ultimately leading to a design that does not meet expectations. Therefore, ensuring the accuracy of the input sample dataset has become a pressing technical problem to be solved. Summary of the Invention

[0004] This application aims to address at least one of the technical problems existing in the prior art. To this end, this application proposes a supercritical airfoil sample sampling method and storage medium for machine learning, which can ensure the accuracy of the sample dataset, thereby enabling the design model established by machine learning to design airfoils that meet the requirements.

[0005] A supercritical airfoil sample sampling method for machine learning according to a first aspect embodiment of this application includes:

[0006] A sampling region is obtained, and sampling is performed based on the sampling region to obtain a target sample set. The sampling region includes multiple initial supercritical airfoil samples that can be sampled, and the target sample set includes multiple target samples obtained by sampling the initial supercritical airfoil samples.

[0007] Based on each expected sample, multiple initial curves corresponding to the airfoil are randomly generated, and a set of initial control point coordinates corresponding to the multiple initial curves is obtained.

[0008] For each expected sample, the airfoil is optimized using a multi-objective genetic algorithm on the corresponding set of multiple initial control point coordinates to obtain the estimated control point coordinates corresponding to the expected sample.

[0009] The coordinates of the multiple estimated control points are mapped and valued using the fluttering proxy model and the drag divergence proxy model, respectively, to obtain an estimated sample set that corresponds one-to-one with the expected sample set.

[0010] Based on the estimated sample set, a target sample set is calculated, and the data format of the target sample set is processed into a surface pressure distribution map that can be used for machine learning. The target sample set includes multiple supercritical airfoil target samples.

[0011] According to some embodiments of this application, the acquisition of the sampling area includes:

[0012] The coordinates and weighting coefficients of the second control point in the second curve are perturbed to adjust the second curve;

[0013] The adjusted second curve is used as a derived airfoil sample, and a geometrically uniform dataset is constructed based on multiple derived airfoil samples;

[0014] CFD calculations are performed on each of the derived airfoil samples to obtain a second calculation result. The second calculation result is then processed to obtain the geometric buffeting lift coefficient and geometric drag divergence evaluation parameters corresponding to the derived airfoil sample.

[0015] Based on multiple geometric buffeting lift coefficients and multiple geometric drag divergence characteristic evaluation coefficients, a lateral sampling region and a longitudinal sampling region are constructed respectively, and the sampling region is determined based on the lateral sampling region and the longitudinal sampling region.

[0016] According to some embodiments of this application, the jitter proxy model is obtained through the following steps:

[0017] The multiple geometric chattering lift coefficients are used as a first mapping array, and the coordinates of each second control point are used as a separate second mapping array.

[0018] The mapping relationship between the first mapping array and the second mapping array is established to obtain the jitter proxy model.

[0019] According to some embodiments of this application, the resistance divergence proxy model is obtained by the following steps:

[0020] The multiple geometric resistance divergence characteristic evaluation coefficients are used as a third mapping array, and the coordinates of each second control point are used as a separate second mapping array.

[0021] The mapping relationship between the third mapping array and the second mapping array is established to obtain the resistance divergence proxy model.

[0022] According to some embodiments of this application, the step of sampling according to the sampling region to obtain a desired sample set includes:

[0023] The expected sample set is obtained by sampling in the sampling area with the goal of uniformly distributing multiple expected samples. The uniform distribution of the expected samples indicates that the expected flutter lift coefficient and the expected drag divergence characteristic evaluation coefficient in the expected samples are uniformly distributed in the sampling area.

[0024] According to some embodiments of this application, the step of randomly generating initial curves corresponding to multiple airfoils based on each expected sample includes:

[0025] The value range of the initial curve is set according to the expected buffeting lift coefficient and the expected drag divergence characteristic evaluation coefficient in each expected sample.

[0026] The initial curve is generated based on the value range and multiple parameters are obtained from the initial curve.

[0027] According to some embodiments of this application, the step of calculating a target sample set based on the estimated sample set and processing the data format of the target sample set into a surface pressure distribution map suitable for machine learning includes:

[0028] CFD calculation is performed on the first curve corresponding to the estimated control point coordinate set to obtain a first calculation result. The first calculation result is then processed to obtain a processed target dataset. The estimated control point coordinate set includes multiple estimated control point coordinates. The first curve is generated from the first control point coordinate set corresponding to the estimated sample set. The first control point coordinate set is obtained through the estimated sample set.

[0029] The target dataset is described by the symbolic distance function to obtain a surface pressure distribution map for machine learning.

[0030] According to some embodiments of this application, before describing the target dataset using a signed distance function to obtain a surface pressure distribution map for machine learning, the method further includes:

[0031] The target dataset is compared and verified with the expected sample set to obtain the verification results;

[0032] If the verification result represents an error within a preset range, then the target dataset passes the verification.

[0033] According to some embodiments of this application, the estimation sample set includes multiple estimation samples, each of which includes an estimated buffeting lift coefficient and an estimated drag divergence characteristic evaluation coefficient.

[0034] The first curve corresponding to the estimated control point coordinate set is subjected to CFD calculation to obtain a first calculation result, and the first calculation result is processed to obtain a processed target dataset, including:

[0035] CFD calculations are performed on the estimated buffeting lift coefficient and the estimated drag divergence characteristic evaluation coefficient to obtain the first lift coefficient and the first drag coefficient.

[0036] The first lift coefficient and the first drag coefficient are processed according to the preset evaluation rules to obtain the target flutter lift coefficient and the target drag divergence characteristic evaluation coefficient, and the target dataset is created based on the target flutter lift coefficient and the target drag divergence characteristic evaluation coefficient.

[0037] A supercritical airfoil sample sampling system according to a second aspect embodiment of this application includes:

[0038] At least one memory;

[0039] At least one processor;

[0040] At least one program;

[0041] The program is stored in the memory, and the processor executes at least one of the programs to implement the method as described in the first aspect embodiment.

[0042] According to a third aspect embodiment of the present application, a computer-readable storage medium stores computer-executable instructions for causing a computer to perform the method described in the first aspect embodiment.

[0043] The supercritical airfoil sample sampling method for machine learning according to the embodiments of this application has the following beneficial effects: First, a sampling area is obtained, and sampling is performed according to the sampling area to obtain an expected sample set, wherein the expected sample set includes multiple expected samples; Second, according to each expected sample, multiple initial curves corresponding to the airfoil are randomly generated, and a set of initial control point coordinates corresponding to the multiple initial curves is obtained; Then, for each expected sample, the airfoil is optimized according to a multi-objective genetic algorithm on the corresponding multiple initial control point coordinate sets to obtain the estimated control point coordinates corresponding to the expected sample; Then, the multiple estimated control point coordinates are mapped and valued respectively through a fluttering proxy model and a drag divergence proxy model to obtain an estimated sample set that corresponds one-to-one with the expected sample set; Finally, a target sample set is calculated according to the estimated sample set, and the data format of the target sample set is processed into a surface pressure distribution map that can be used for machine learning. The supercritical airfoil sample sampling method of this application involves setting a sampling area and sampling to obtain a target sample set. Then, a first curve is generated from the target samples in the target sample set to obtain a first control point coordinate set composed of the coordinates of the first control points. The estimated sample set is then obtained through processing by a multi-objective genetic algorithm, a fluttering proxy model, and a drag divergence proxy model. Based on the estimated sample set, a surface pressure distribution map for machine learning is calculated. Through the above processing, the accuracy of the sample dataset can be effectively guaranteed, thereby enabling the design model established by machine learning to design an airfoil that meets the requirements.

[0044] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0045] The present application will be further described below with reference to the accompanying drawings and embodiments, wherein:

[0046] Figure 1 This is a flowchart illustrating a supercritical airfoil sample sampling method for machine learning provided in one embodiment of this application.

[0047] Figure 2 This is a schematic diagram illustrating the overall process of a supercritical airfoil sample sampling method for machine learning provided in one embodiment of this application.

[0048] Figure 3 This is an airfoil distribution diagram of a geometrically uniform dataset provided in one embodiment of this application;

[0049] Figure 4 The distribution diagram of the buffeting lift coefficient and drag divergence characteristic evaluation coefficient of the geometrically uniform dataset provided in one embodiment of this application;

[0050] Figure 5 A distribution diagram of the buffeting lift coefficient and drag divergence characteristic evaluation coefficient of a performance uniform distribution expected sample set provided in an embodiment of this application;

[0051] Figure 6 The distribution of the buffeting lift coefficient and drag divergence characteristic evaluation coefficient of the estimated sample set provided in one embodiment of this application;

[0052] Figure 7 The distribution of buffeting lift coefficient and drag divergence characteristic evaluation coefficient obtained after CFD calculation and evaluation is provided in one embodiment of this application;

[0053] Figure 8 This is a supercritical airfoil geometry provided in one embodiment of this application;

[0054] Figure 9 This is a critical airfoil surface pressure distribution diagram provided in one embodiment of this application;

[0055] Figure 10 This is a graph showing the rate of change of the slope of the lift curve provided in one embodiment of this application;

[0056] Figure 11 This is a graph showing the lift-to-drag ratio versus Mach number with a fixed lift coefficient, provided in one embodiment of this application.

[0057] Figure 12 This is a schematic diagram of the structure of a supercritical airfoil sample sampling system provided in one embodiment of this application.

[0058] Figure label:

[0059] Memory 200, processor 300. Detailed Implementation

[0060] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0061] It should be noted that although functional modules are divided in the system diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the system or the order in the flowchart. The terminology in the specification, claims, and the foregoing figures is used to distinguish similar objects and is not necessarily used to describe a specific order or sequence.

[0062] In the description of this application, "several" means one or more, "multiple" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0063] In the description of this application, unless otherwise expressly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0064] In the description of this application, the terms "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0065] The following are explanations of some of the terms:

[0066] Lift: The projection of the pressure difference caused by the velocity difference between the upper and lower surfaces of the aerodynamic shape along the direction perpendicular to the incoming flow.

[0067] Resistance: The force generated by an object moving relative to a fluid in the opposite direction of its motion; that is, the projection of the force exerted by the airflow on the surface of the object along the direction of the incoming flow.

[0068] Lift coefficient: The ratio of lift to the product of air pressure and reference area; dimensionless.

[0069] Drag coefficient; the ratio of drag to the product of air pressure and reference area, dimensionless.

[0070] Lift-to-drag ratio: The ratio of the lift coefficient to the drag coefficient.

[0071] Airfoil: Generally refers to a two-dimensional airfoil, that is, an airfoil with an infinite wingspan and an unchanged cross-sectional shape. Airfoil design includes forward design and reverse design. Forward design refers to obtaining aerodynamic performance from an airfoil geometry; reverse design refers to obtaining airfoil geometry from an airfoil geometry through iterative modification based on its aerodynamic performance.

[0072] Aerodynamic characteristics: The laws governing the variation of aerodynamic forces and moments acting on an aircraft with parameters such as aircraft geometry, flight attitude, speed, and atmospheric density. Parameters used to describe aerodynamic characteristics include: lift coefficient, drag coefficient, moment coefficient, and lift-to-drag ratio.

[0073] Supercritical airfoils: Airfoils designed to increase the critical Mach number, widely used in transonic aircraft such as commercial airliners. Their main function is to enable aircraft to achieve higher cruising speeds during subsonic flight, while ensuring safety, durability, and economy.

[0074] Buffeting: Irregular vibrations of a structure or part of a structure induced by boundary layer separation or turbulence. For supercritical airfoils, the primary concern is buffeting caused by shock waves at transonic speeds. Buffeting leads to lift loss, increases flight safety risks, and in severe cases, can cause the aircraft to disintegrate in mid-air.

[0075] Drag divergence: Due to the compressibility of air, when the airflow passes over the upper surface of a supercritical airfoil, it accelerates locally beyond the speed of sound, generating a strong shock wave, which causes a surge in drag.

[0076] Drag divergence Mach number: refers to the Mach number at which the partial derivative of the drag coefficient with respect to the free-flow Mach number is equal to 0.1 when the drag coefficient changes with the free-flow Mach number.

[0077] Latin hypercube sampling (LHS) is a method of approximately random sampling from a multi-parameter distribution. It is a method of stratified sampling in statistics.

[0078] C2 continuity: Second-order continuous and differentiable at the junction. Also known as curvature continuity. This is a description of the smoothness of a function in computer graphics, and the term is documented in the third edition of *Computer Science and Technology Terminology* (Science Press).

[0079] CFD (Computational Fluid Dynamics) is a product of the combination of modern fluid mechanics, numerical mathematics, and computer science. It is a highly dynamic interdisciplinary science. It approximates the integral and differential terms in the governing equations of fluid mechanics as discrete algebraic forms, making them a system of algebraic equations. Then, it uses computers to solve these discrete algebraic equations to obtain numerical solutions at discrete time / space points.

[0080] Among related technologies, machine learning is a discipline developed based on mathematical disciplines such as probability theory and statistics. Therefore, sample datasets are fundamental to machine learning. Relatively speaking, the application of machine learning in the aerospace field started late and developed slowly. This is mainly because relevant, reliable data often needs to be obtained through experiments, which is difficult and costly. Currently, researchers primarily use computational fluid dynamics methods to calculate airfoil performance through numerical simulations as reference data for design. The training results of machine learning are inseparable from the quality of the sample dataset; the quantity and distribution of samples often directly determine the training results. Therefore, a large amount of data is generally required for training to obtain a high-performance model.

[0081] Supercritical airfoils are airfoils designed to increase the critical Mach number. They delay the dramatic increase in drag that occurs near the speed of sound, thus increasing the aircraft's cruise speed. They are widely used in transonic aircraft, such as commercial airliners. Currently, the cruise speeds of commercial airliners are all in the transonic range. In this speed range, shock waves appearing on the wing can induce boundary layer separation, causing periodic shock wave oscillations, i.e., buffeting. Buffeting can generate unstable structural stresses in the airframe, reducing the aircraft's fatigue life and, in severe cases, potentially leading to in-flight disintegration. Meanwhile, the drag divergence Mach number, which represents the Mach number at which drag surges with increasing speed, is a key parameter limiting the cruise speed of supercritical airfoils.

[0082] In aerodynamics, an airfoil typically refers to a two-dimensional wing, that is, an infinitely spanned wing with a constant cross-sectional shape. When an airfoil moves relative to the air, its surface is subjected to forces from the airflow. The component of the resultant force in the direction of the incoming flow is drag, and the component perpendicular to the drag is lift. The moment generated by these forces relative to the center of mass, causing the airfoil to pitch, is called the pitching moment. The lift coefficient and drag coefficient are dimensionless numbers used to describe the lift and drag effects on the airfoil, respectively. Typically, the parameters describing the aerodynamic characteristics of an airfoil (referred to as launch parameters) mainly include the lift coefficient, drag coefficient, moment coefficient, and lift-to-drag ratio at different angles of attack.

[0083] For a long time, airfoil design has involved selecting airfoils with performance close to the target from an existing airfoil library, and then undergoing several rounds of modification and iteration to finally obtain an airfoil that meets the expected goals. However, the correlation between many flow phenomena and the local geometric features of the airfoil remains unclear. Therefore, a method is needed that can: in forward airfoil design, quickly and accurately obtain the aerodynamic parameters of the airfoil based on its geometry; in reverse airfoil design, quickly obtain a batch of airfoil geometries that meet the conditions based on the most important aerodynamic performance, or guide local modification based on characteristics under specific conditions, such as buffeting characteristics. Machine learning provides excellent technical support for solving such problems, but how to establish a sample dataset for machine learning and ensure the speed and accuracy of design models built based on machine learning is a technical problem that needs to be solved.

[0084] To address the aforementioned issues, this application provides a supercritical airfoil sample sampling method based on the fluttering and drag divergence characteristics of supercritical airfoils. This method enables the batch collection of a large number of diverse airfoil sample data in a short time, while ensuring that the data meets the format requirements of existing machine learning frameworks.

[0085] The following reference Figure 1 This application describes a supercritical airfoil sample sampling method according to an embodiment.

[0086] Understandably, referring to Figure 1 A method for sampling supercritical airfoil samples is provided, including:

[0087] Step S100: Obtain the sampling area and perform sampling based on the sampling area to obtain the expected sample set. The sampling area includes multiple initial supercritical airfoil samples that can be sampled, and the expected sample set includes multiple expected samples obtained by sampling the initial supercritical airfoil samples.

[0088] Step S110: Based on each expected sample, randomly generate multiple initial curves corresponding to the airfoil, and obtain the initial control point coordinate set corresponding to the multiple initial curves.

[0089] Step S120: For each expected sample, the airfoil is optimized using a multi-objective genetic algorithm on the corresponding set of multiple initial control point coordinates to obtain the estimated control point coordinates corresponding to the expected sample.

[0090] Step S130: Map the coordinates of multiple estimated control points through the fluttering proxy model and the drag divergence proxy model to obtain the estimated sample set that corresponds one-to-one with the expected sample set.

[0091] Step S140: Calculate the target sample set based on the estimated sample set, and process the data format of the target sample set into a surface pressure distribution map that can be used for machine learning. The target sample set includes multiple supercritical airfoil target samples.

[0092] First, a sampling region is acquired, and sampling is performed based on this region to obtain a target sample set, which includes multiple target samples. Second, for each target sample, multiple initial curves corresponding to different airfoils are randomly generated, and a set of initial control point coordinates corresponding to these initial curves is obtained. Then, for each target sample, an airfoil optimization algorithm is used to optimize the corresponding set of initial control point coordinates, resulting in estimated control point coordinates. Next, the estimated control point coordinates are mapped using a fluttering proxy model and a drag divergence proxy model to obtain estimated sample sets that correspond one-to-one with the target sample set. Finally, based on the estimated sample set, a target sample set is calculated, and the data format of the target sample set is processed into a surface pressure distribution map suitable for machine learning. The supercritical airfoil sample sampling method of this application involves setting a sampling area and sampling to obtain a target sample set. Then, a first curve is generated from the target samples in the target sample set to obtain a first control point coordinate set composed of the coordinates of the first control points. The estimated sample set is then obtained through processing by a multi-objective genetic algorithm, a fluttering proxy model, and a drag divergence proxy model. Based on the estimated sample set, a surface pressure distribution map for machine learning is calculated. Through the above processing, the accuracy of the sample dataset can be effectively guaranteed, thereby enabling the design model established by machine learning to design an airfoil that meets the requirements.

[0093] It should be noted that the initial curve is the first non-uniform rational B-spline curve (NURBS curve).

[0094] Specifically, the NURBS curve fitting formula is as follows:

[0095]

[0096] Specifically:

[0097]

[0098]

[0099] in:

[0100] P i w represents the coordinates of the control point. i These are the weight coefficients, belonging to set S respectively. CP ={P i =(x i ,y i )|0≤i≤n}, and W={wi |0≤i≤n}。 N i，p (u) is a k-th degree B-spline basis function, which is formed by the node vector U = [U0, U1, ..., U...]. m ], m=n+p+1, the recurrence relation for the p-th degree piecewise polynomial is:

[0101]

[0102] In particular,

[0103]

[0104]

[0105] It is understandable that the sampling area includes:

[0106] The coordinates and weighting coefficients of the second control point in the second curve are perturbed to adjust the second curve;

[0107] The adjusted second curve is used as a derived airfoil sample, and a geometrically uniform dataset is constructed based on multiple derived airfoil samples.

[0108] For each derived airfoil sample, CFD calculation is performed to obtain a second calculation result. The second calculation result is then processed to obtain the geometric buffeting lift coefficient and geometric drag divergence evaluation parameters corresponding to the derived airfoil sample.

[0109] Based on multiple geometric buffeting lift coefficients and multiple geometric drag divergence characteristic evaluation coefficients, lateral and longitudinal sampling regions are constructed respectively, and the sampling region is determined based on the lateral and longitudinal sampling regions.

[0110] It should be noted that the derived airfoil sample can be understood as the initial sample of the supercritical airfoil. By sampling to obtain a geometrically uniform dataset, and constructing a sampling region based on multiple derived airfoil samples in the geometrically uniform dataset, the validity of the expected sample obtained by sampling can be effectively guaranteed.

[0111] It should be noted that the drag divergence evaluation parameter is used to describe the drag divergence phenomenon. In this invention, it is a function of the average lift-to-drag ratio and the Mach number.

[0112] It should be noted that the second curve is the second NURBS curve.

[0113] It should be noted that, in order to ensure the C2 continuity of the airfoil curve, sampling is performed using 18 control points of the NURBS curve and corresponding weight coefficients to generate geometrically uniform derivative airfoil samples, forming a geometrically uniform dataset.

[0114] Understandably, based on the estimated sample set, the target sample set is calculated, and the data format of the target sample set is processed into a surface pressure distribution map suitable for machine learning, including:

[0115] CFD calculation is performed on the first curve corresponding to the estimated control point coordinate set to obtain the first calculation result. The first calculation result is then processed to obtain the processed target dataset. The estimated control point coordinate set includes multiple estimated control point coordinates. The first curve is generated from the first control point coordinate set corresponding to the estimated sample set. The first control point coordinate set is obtained through the estimated sample set.

[0116] The target dataset is described by the symbolic distance function to obtain a surface pressure distribution map for machine learning.

[0117] It should be noted that the symbolic distance function is as follows:

[0118]

[0119] in:

[0120] (x i ,y j (x) represents the coordinates of a point in space. Γ ,y Γ ) indicates to (x i ,y j The coordinates of the nearest point on the airfoil.

[0121] Understandably, before describing the target dataset using the signed distance function to obtain the surface pressure distribution map for machine learning, the following steps are also included:

[0122] The target dataset is compared with the expected sample set to obtain the verification results;

[0123] If the verification result represents the error within a preset range, the target dataset passes the verification.

[0124] It should be noted that comparative validation is to verify the error between the target dataset and the expected sample set.

[0125] It is understandable that the estimation sample set includes multiple estimation samples, and each estimation sample includes the estimated buffeting lift coefficient and the estimated drag divergence characteristic evaluation coefficient.

[0126] CFD calculations are performed on the first curve corresponding to the estimated control point coordinate set to obtain the first calculation result. The first calculation result is then processed to obtain the processed target dataset, including:

[0127] CFD calculations were performed on the estimated buffeting lift coefficient and the estimated drag divergence characteristic evaluation coefficient to obtain the first lift coefficient and the first drag coefficient.

[0128] The first lift coefficient and the first drag coefficient are processed according to the preset evaluation rules to obtain the target flutter lift coefficient and the target drag divergence characteristic evaluation coefficient, and a target dataset is created based on the target flutter lift coefficient and the target drag divergence characteristic evaluation coefficient.

[0129] It should be noted that, as Figure 2 As shown, airfoil design includes forward and reverse designs.

[0130] In forward design:

[0131] Multiple second curves are obtained by perturbing the coordinates and weighting coefficients of the second control points in the second curve; this method is the Latin hypercube sampling method. Simultaneously, the distribution interval of the second curves should conform to… Figure 2 The distribution interval is set; a geometrically uniform dataset is obtained by establishing multiple second curves;

[0132] CFD calculations are performed on each derived airfoil sample in the geometrically uniform dataset to obtain a second calculation result, which includes a second lift coefficient and a second drag coefficient. The second lift coefficient and the second drag coefficient are processed by the evaluation rules to obtain the geometric buffeting lift coefficient and geometric drag divergence characteristic evaluation coefficient corresponding to the derived airfoil sample.

[0133] In reverse engineering:

[0134] The sampling area is determined based on the geometric buffeting lift coefficient and geometric drag divergence characteristic evaluation coefficient obtained from the forward design, and sampling is performed within the sampling area to obtain the expected sample set.

[0135] For each expected sample in the expected sample set, generate multiple initial curves;

[0136] The initial curve is optimized using a multi-objective genetic algorithm, and an estimated sample set is obtained based on the mapping of the surrogate model.

[0137] CFD calculations are performed on the estimated sample set to obtain the first lift coefficient and the first drag coefficient. Then, the target buffet lift coefficient and the target drag divergence characteristic evaluation coefficient are obtained through the evaluation rules.

[0138] It should be noted that geometrically uniform datasets, such as Figure 3 As shown, the estimated evaluation coefficients for the buffeting lift coefficient and drag divergence characteristics of the sample set are as follows: Figure 4 As shown.

[0139] It should be noted that the expected sample set is as follows: Figure 5As shown, the distribution is a uniform rectangular shape. Figure 5 The expected sample distribution is given with the mean of the buffeting lift coefficient at Reynolds number Re = 16,000,000 and Mach number Ma = 0.73, and the lift-to-drag ratio at Mach numbers Ma of 0.71, 0.72, 0.73, 0.74, 0.75 and lift coefficient Cl = 0.83 as the target.

[0140] It should be noted that the estimated sample set is as follows: Figure 6 As shown.

[0141] It should be noted that the distribution of the target buffeting lift coefficient and the target drag divergence characteristic evaluation coefficient is as follows: Figure 7 As shown.

[0142] It should be noted that by describing the geometrically uniform dataset using the signed distance function, the following results are obtained: Figure 8 The diagram shows the geometry of a supercritical airfoil.

[0143] It should be noted that the surface pressure distribution map obtained by describing the target dataset using the signed distance function is as follows: Figure 9 As shown,

[0144] It should be noted that the first and second calculation results are verified according to the evaluation rules. The specific steps are as follows:

[0145] The first calculation result includes a first lift coefficient and a first drag coefficient, and the second calculation result includes a second lift coefficient and a second drag coefficient.

[0146] Define the evaluation rules, which are the initial boundary criteria and evaluation metrics for chattering:

[0147] The initial boundary criterion for the buffeting of the airfoil is defined as the angle of attack at which the rate of change of the lift line slope changes significantly, and the lift coefficient at the initial buffeting angle of attack is used as the buffeting lift coefficient. The drag divergence characteristic evaluation function of the airfoil is defined, and the average lift-to-drag ratio at 5 different Mach numbers and the same lift coefficient is used as the evaluation index.

[0148] In the CFD calculation process, multiple first lift coefficients are obtained by changing the angle of attack. When two adjacent first lift coefficients change drastically, the first lift coefficient at the point of drastic change is determined as the buffeting lift coefficient. For illustrative purposes, as follows... Figure 10 As shown, the buffeting lift coefficient is the lift coefficient corresponding to an angle of attack between 2 degrees and 2.5 degrees; the calculation process for the second lift coefficient is the same as that for the first lift coefficient, and will not be repeated here.

[0149] like Figure 11As shown, with the lift coefficient set at 0.83, the drag divergence characteristic evaluation coefficients are calculated at different Mach numbers.

[0150] The lift-to-drag ratio is calculated as 0.83 / first drag coefficient. After calculating multiple lift-to-drag ratios, the average value is taken to obtain the final drag divergence characteristic evaluation coefficient.

[0151] The relevant tables are as follows:

[0152] Mach number Ma 0.71 0.72 0.73 0.74 0.75 Boost-to-drag ratio K 65.8979 60.2410 53.0504 44.8682 38.1134

[0153] Evaluation coefficient of drag divergence characteristics:

[0154]

[0155] The calculation process for the second drag coefficient is the same as that for the first drag coefficient, and will not be repeated here.

[0156] Understandably, the jitter proxy model is obtained through the following steps:

[0157] Multiple geometric buffeting lift coefficients are used as the first mapping array, and the coordinates of each second control point are used as a separate second mapping array.

[0158] Establish the mapping relationship between the first mapping array and the second mapping array to obtain the jitter proxy model.

[0159] It should be noted that the jitter proxy model is the Kriging proxy model.

[0160] Understandably, the resistance divergence surrogate model is derived from the following steps:

[0161] Multiple geometric resistance divergence characteristic evaluation coefficients are used as the third mapping array, and the coordinates of each second control point are used as a separate second mapping array.

[0162] By establishing the mapping relationship between the third mapping array and the second mapping array, the resistance divergence surrogate model is obtained.

[0163] It should be noted that the resistance divergence surrogate model is the Anisotropic Kriging surrogate model.

[0164] It is understandable that sampling is performed based on the sampling area to obtain the expected sample set, including:

[0165] Sampling is performed in the sampling area with the goal of uniformly distributing multiple expected samples to obtain the expected sample set. The uniform distribution of expected samples indicates that the expected flutter lift coefficient and the expected drag divergence characteristic evaluation coefficient in the expected samples are uniformly distributed in the sampling area.

[0166] It should be noted that,

[0167] Understandably, based on each expected sample, multiple initial curves corresponding to the airfoil are randomly generated, including:

[0168] The initial curve's value range is set based on the expected buffeting lift coefficient and expected drag divergence characteristic evaluation coefficient in each expected sample.

[0169] Obtain multiple parameters from the initial curve based on the value range, and generate the initial curve based on the multiple parameters.

[0170] The following reference Figure 12 This application describes a supercritical airfoil sample sampling system according to an embodiment of the present application.

[0171] It is understandable that, such as Figure 12 As shown, the supercritical airfoil sample sampling system includes:

[0172] At least one memory 200;

[0173] At least one processor 300;

[0174] At least one program;

[0175] The program is stored in memory 200, and processor 300 executes at least one program to implement the supercritical airfoil sample sampling method described above. Figure 12 Take a processor 300 as an example.

[0176] The processor 300 and the memory 200 can be connected via a bus or other means. Figure 12 Take a bus connection as an example.

[0177] The memory 200, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and signals, such as the program instructions / signals corresponding to the supercritical airfoil sample sampling system in this embodiment. The processor 300 executes various functional applications and data processing by running the non-transitory software programs, instructions, and signals stored in the memory 200, thereby implementing the supercritical airfoil sample sampling method of the above-described method embodiment.

[0178] The memory 200 may include a program storage area and a data storage area. The program storage area may store the operating system and application programs required for at least one function; the data storage area may store relevant data of the supercritical airfoil sample sampling method described above. Furthermore, the memory 200 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory 200 may optionally include memory remotely located relative to the processor 300, and these remote memories can be connected to the supercritical airfoil sample sampling system via a network. Examples of such networks include, but are not limited to, the Internet of Things (IoT), software-defined networks, sensor networks, the Internet, enterprise intranets, local area networks (LANs), mobile communication networks, and combinations thereof.

[0179] One or more signals are stored in memory 200, and when executed by one or more processors 300, the supercritical airfoil sample sampling method in any of the above method embodiments is performed. For example, the above-described... Figure 1 The method in the middle.

[0180] The following reference Figure 12 This application describes a computer-readable storage medium according to embodiments thereof.

[0181] like Figure 12 As shown, a computer-readable storage medium stores computer-executable instructions that are executed by one or more processors 300, for example, by... Figure 12 One or more processors 300 may execute the supercritical airfoil sample sampling method described in the above method embodiments. For example, the method described above may be executed. Figure 1 The method in the middle.

[0182] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0183] Based on the above description of the embodiments, those skilled in the art will understand that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media and communication media. As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital multifunction disk or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is known to those skilled in the art that communication media typically contain computer-readable signals, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and can include any information delivery medium.

[0184] The embodiments of this application have been described in detail above with reference to the accompanying drawings. However, this application is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of this application. Furthermore, unless otherwise specified, the embodiments and features described in the embodiments of this application can be combined with each other.

Claims

1. A supercritical airfoil sample sampling method for machine learning, characterized in that, include: A sampling region is obtained, and sampling is performed based on the sampling region to obtain a target sample set. The sampling region includes multiple initial supercritical airfoil samples that can be sampled, and the target sample set includes multiple target samples obtained by sampling the initial supercritical airfoil samples. Based on each expected sample, multiple initial curves corresponding to the airfoil are randomly generated, and a set of initial control point coordinates corresponding to the multiple initial curves is obtained. For each expected sample, the airfoil is optimized using a multi-objective genetic algorithm on the corresponding set of multiple initial control point coordinates to obtain the estimated control point coordinates corresponding to the expected sample. The coordinates of the multiple estimated control points are mapped and valued using the buffeting proxy model and the drag divergence proxy model, respectively, to obtain an estimated sample set that corresponds one-to-one with the expected sample set; the estimated sample set includes multiple estimated samples, and each estimated sample includes an estimated buffeting lift coefficient and an estimated drag divergence characteristic evaluation coefficient. CFD calculations are performed on the estimated buffeting lift coefficient and the estimated drag divergence characteristic evaluation coefficient to obtain the first lift coefficient and the first drag coefficient. The first lift coefficient and the first drag coefficient are processed according to preset evaluation rules to obtain the target flutter lift coefficient and the target drag divergence characteristic evaluation coefficient, and a target dataset is created based on the target flutter lift coefficient and the target drag divergence characteristic evaluation coefficient; The target dataset is described by the signed distance function to obtain a surface pressure distribution map for machine learning. The sampling area includes: The coordinates and weighting coefficients of the second control point in the second curve are perturbed to adjust the second curve; The adjusted second curve is used as a derived airfoil sample, and a geometrically uniform dataset is constructed based on multiple derived airfoil samples; CFD calculations are performed on each of the derived airfoil samples to obtain a second calculation result. The second calculation result is then processed to obtain the geometric flutter lift coefficient and geometric drag divergence characteristic evaluation coefficient corresponding to the derived airfoil sample. Based on multiple geometric buffeting lift coefficients and multiple geometric drag divergence characteristic evaluation coefficients, a lateral sampling region and a longitudinal sampling region are constructed respectively, and the sampling region is determined based on the lateral sampling region and the longitudinal sampling region. The jitter proxy model is obtained through the following steps: The multiple geometric chattering lift coefficients are used as a first mapping array, and the coordinates of each second control point are used as a separate second mapping array. Establish the mapping relationship between the first mapping array and the second mapping array to obtain the jitter proxy model; The resistance divergence proxy model is obtained through the following steps: The multiple geometric resistance divergence characteristic evaluation coefficients are used as a third mapping array, and the coordinates of each second control point are used as a separate second mapping array. The mapping relationship between the third mapping array and the second mapping array is established to obtain the resistance divergence proxy model.

2. The supercritical airfoil sample sampling method according to claim 1, characterized in that, The step of sampling according to the sampling region to obtain the expected sample set includes: The expected sample set is obtained by sampling in the sampling area with the goal of uniformly distributing multiple expected samples. The uniform distribution of the expected samples indicates that the expected flutter lift coefficient and the expected drag divergence characteristic evaluation coefficient in the expected samples are uniformly distributed in the sampling area.

3. The supercritical airfoil sample sampling method according to claim 2, characterized in that, The step of randomly generating multiple initial curves corresponding to each airfoil based on each expected sample includes: The value range of the initial curve is set according to the expected buffeting lift coefficient and the expected drag divergence characteristic evaluation coefficient in each expected sample. The initial curve is generated based on the value range and multiple parameters are obtained from the initial curve.

4. The supercritical airfoil sample sampling method according to claim 1, characterized in that, Before describing the target dataset using the signed distance function to obtain a surface pressure distribution map for machine learning, the method further includes: The target dataset is compared and verified with the expected sample set to obtain the verification results; If the verification result represents an error within a preset range, then the target dataset passes the verification.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions for causing a computer to perform the method as described in any one of claims 1 to 4.

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